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# Finding Point-Slope Equations

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### Finding Point-Slope Equations

1. 1. Writing Point-Slope Equations<br />Algebra II<br />By: Jordan Malone<br />Image courtesy of Microsoft Word Clipart collection<br />
2. 2. Standard Form<br />y = mx + b <br />m = slope<br />b = y-intercept<br />
3. 3. How to Find Slope<br />
4. 4. Try it yourself!<br />Find the slope (m) between the two points (3, 4) and (-8, 5).<br />m = -11<br />
5. 5. Try it yourself!<br />Find the slope using <br />the graph below.<br />(2,4)<br />(-4,-2)<br />m = 1<br />
6. 6. Finding y-intercept<br />By definition, “In coordinate geometry, the y-intercept is the y-value of the point where the graph of a function or relation intercepts the y-axis of the coordinate system.”<br />Definition found at en.wikipedia.org/wiki/Y-intercept<br />
7. 7. Try it yourself!<br />Use the graph to <br />find the y-intercept.<br />b = (0,1)<br />x-coordinate <br />will always <br />be zero<br />
8. 8. Try it yourself!<br />Write the point-slope equation for the line with slope of -½ and y-intercept of 5.<br />m = -½<br />b = 5 <br />y = -½x + 5<br />Plug into equation<br />
9. 9. Try it yourself!<br />Given the points (1,2) and (4,3), and y-intercept of 5/3, write the point-slope equation of the line.<br />2.) Plug the slope into the equation next with the given y-intercept.<br />1.) Find the slope using the two given points.<br />
10. 10. Write the point-slope equation using the graph below.<br />Try it yourself!<br />1.) Find the y-intercept.<br />b = (0,-2)<br />2.) Find the slope by starting at the y-intercept, and counting up and over until you hit another point on the line. (rise over run)<br />We can count up 1, and left 1, and hit another point on the line, so the slope = 1/1. Plug into equation.<br />2<br />1<br />-1<br />-2<br />y = 1x - 2<br />
11. 11. Undefined vs. Zero Slopes<br />
12. 12. What do two parallel lines have in common?<br />Two parallel lines share the same slope, but pass through a different set of points<br />
13. 13. Let’s look at some graphs of parallel lines…<br />Slope of line 1: 0<br />Slope of line 2: 0<br />Slope of line 1: undefined<br />Slope of line 2: undefined<br />
14. 14. Writing point-slope equations using parallel lines<br />Write the point-slope equations for each line given the points below.<br />Line 1: (2,3) and (4,6), b = 0 <br />Line 2: (5,6) and (7,9), b = -3/2<br />y = 3/2x + 0 <br />y = 3/2x -3/2<br />
15. 15. Using an equation to write another that is parallel to it…<br />Given y = 4x + 1, write the equation of its parallel line that passes through the point (1,3).<br />Since the slopes are the same, we will start by writing <br />y = 4x + b.<br />Next, solve for b by plugging in the point given. <br />x = 1, and y = 3, so 3 = 4(1) + b.<br />Solving for b, we get b = -1. To finish the problem, we will plug b into our original equation shown in blue.<br />y = 4x - 1 <br />
16. 16. Try it yourself!<br />Use the graph to find the equation of the line parallel to it that passes through <br />(-3, -6). Then graph it.<br />First, find the slope of the given line using rise over run. <br />m = (-4/2)<br />Plug into y = mx + b and solve for b by using the point given.<br />x = -3, y = -6<br />-6 = (-4/2)(-6) + b<br />b = -12<br />4<br />2<br />y = (-4/2)x - 12 <br />
17. 17. Exit Questions<br />What is the y-intercept?<br />What is the point-slope equation in general?<br />Find the slope between points (-1,1) and (3,-4).<br />What do parallel lines have in common?<br />